"I know that a lot of people find appeal in the things Donald says, 'cause he says what people wish they could say," Rubio responded. "The problem is presidents can't just say anything they want."

Rubio said Trump's remarks about Islam were alienating Muslims in other countries and those at home.

"There is no doubt that radical Islam is a danger in the world," Rubio said, adding that those who visit Arlington National Cemetery will see "crescent moons," on the tombstones of fallen Muslim-American service members.

"Marco talks about consequences, well we've had a lot of consequence," Trump retorted, mentioning the terrorist attacks on Sept. 11, 2001, and saying he didn't want to be "politically correct."

"We have a serious, serious problem of hate," Trump said. "There is tremendous hate ... there is tremendous hatred."

"I'm not interested in being politically correct. I'm interested in being correct," Rubio responded to applause. He argued the U.S. would need to work with majority-Muslim nations like Jordan to defeat the Islamic State in Iraq and Syria.